The example SQL below renames the MySQL table "tablename" to "tablename_renamed":
RENAME TABLE tablename TO tablename_renamed
To rename a MySQL table with phpMyAdmin, select the database then table, and click the "Operations" tab. Then put the new name into the text box labelled "rename table to" and click the "Go" button. The relevent buttons etc are highlighted with red circles in the screenshot below.
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After clicking the "Go" button the table will be renamed and the same page as shown above will be loaded again, showing the rename query that was executed.